We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. We also show that, in the compact case, this criterion implies discreteness of the sub-Laplacian spectrum even though the total volume of the manifold is infinite. As a consequence of our result, the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp’s measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This settles a conjecture formulated by Boscain and Laurent (Ann. Inst. Fourier (Grenoble) 63(5), 1739–1770, 2013), under mild regularity assumptions on the singular region, and when the latter does not contain characteristic points.

On the Essential Self-Adjointness of Singular Sub-Laplacians / Franceschi, V.; Prandi, D.; Rizzi, L.. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 53:(2020), pp. 89-112. [10.1007/s11118-018-09760-w]

On the Essential Self-Adjointness of Singular Sub-Laplacians

Prandi, D.;Rizzi, L.
2020

Abstract

We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. We also show that, in the compact case, this criterion implies discreteness of the sub-Laplacian spectrum even though the total volume of the manifold is infinite. As a consequence of our result, the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp’s measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This settles a conjecture formulated by Boscain and Laurent (Ann. Inst. Fourier (Grenoble) 63(5), 1739–1770, 2013), under mild regularity assumptions on the singular region, and when the latter does not contain characteristic points.
53
89
112
https://arxiv.org/abs/1708.09626
Franceschi, V.; Prandi, D.; Rizzi, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128674
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